For Pre-Classical background and general description of early development of string quartet from various Baroque and early Classical genres, including chamber sonatas, sinfonias see NG XVIII 276–278.
Important in early development are the sinfonias and quartets of G.B. Sammartini. These influenced Mozart and (especially) Boccherini.
More significant are the quartet-symphonies of south German composers—Mannheim from ca. 1745 (J.W.A. Stamitz, F.X. Richter, Holzbauer, Filtz, C. Cannabich, & Eichner)—and divertimentos (Asplmayr, Camerloher, Startzer, Gassmann, & Haydn).
Important early quartets:
M.G. Monn, Six quartets (in DTÖ, XXXIX, Jg.XIX/2).
F. X. Richter, Six quartets, Op. 5 (ca. 1765–1757): quite polyphonic, with active viola & v'cello parts. [Many transitional {Baroque-Classical} string chamber ensemble works of this period are polyphonic. This remained a feature through the works of Haydn.]
Transitional works may have three, four, or five movements. Of these, one or two are often minuets.
During the 1750s & 1760s these works may or may not have figured bass. Gradually, indications of continuo disappear.
Early works show a great variety of textures in different movements: solo, even elaborate 1st violin parts, sometimes with cadenzas; fugal textures.
From 1775, the quartets of Haydn and Mozart "are simply the high points in an intense cultivation of the string quartet in Vienna in the last quarter of the 18th century, which made it a major preoccupation of composers, publishers and performers alike." [NG XVIII 279.]
[For the relatively less important development of the string quartet during the later 18th century in England, France, Spain; and the development of the quatuor brillant and the French quatuor concertant, see NG XV 500–501, XVIII 279–280.]